Explore the intersection of mathematics and computer animation in this 49-minute lunch talk by David Baraff, Principal Software Engineer at Pixar Animation Studios. Delve into the advanced mathematical techniques used to create realistic effects like clothing, hair, water, and 3D interactive animation. Learn about dynamic simulation, rigid body dynamics, constraints, quadratic programming, and the Traveling Salesman Problem. Discover how hair and cloth simulations are modeled and implemented. Gain insights into matrix operations, subdivision surfaces, mesh deformation, and surface exploration. Examine real-world applications in films like Toy Story, Brave, and The Lord of the Rings. Understand the challenges of debugging complex simulations and the importance of efficient searching algorithms in computer animation.